Near-Infrared Spectroscopy for the In Vivo Monitoring of Biodegradable Implants in Rats

Magnesium (Mg) alloys possess unique properties that make them ideal for use as biodegradable implants in clinical applications. However, reports on the in vivo assessment of these alloys are insufficient. Thus, monitoring the degradation of Mg and its alloys in vivo is challenging due to the dynamic process of implant degradation and tissue regeneration. Most current works focus on structural remodeling, but functional assessment is crucial in providing information about physiological changes in tissues, which can be used as an early indicator of healing. Here, we report continuous wave near-infrared spectroscopy (CW NIRS), a non-invasive technique that is potentially helpful in assessing the implant–tissue dynamic interface in a rodent model. The purpose of this study was to investigate the effects on hemoglobin changes and tissue oxygen saturation (StO2) after the implantation of Mg-alloy (WE43) and titanium (Ti) implants in rats’ femurs using a multiwavelength optical probe. Additionally, the effect of changes in the skin on these parameters was evaluated. Lastly, combining NIRS with photoacoustic (PA) imaging provides a more reliable assessment of tissue parameters, which is further correlated with principal component analysis.


Introduction
Biodegradable materials such as magnesium (Mg) and its alloys have increasingly been used in orthopedic surgery for bone fixation [1]. Although the cellular responses of surrounding tissue are important, their mechanism of action remains unclear [2]. Due to their osteogenic properties and biodegradability, Mg implants have been gaining significant attention among degradable materials as a superior alternative to bio-inert implants [3,4]. Titanium alloys are considered the gold standard for stabilizing fractured bones, also referred to as a bio-inert metallic implant [5]. Magnesium hydroxide temporarily inhibits osteoclastic activity and stimulates bone formation, but emphysema can occur if hydrogen gas production exceeds the tissue's ability to absorb and transport the gas [6][7][8]. The formation and composition of the degradation layer alter physiological parameters such as the temperature, pH, ionic content, and protein content after implantation [9]. Currently, imaging techniques such as X-ray imaging, computed tomography (CT), synchrotronradiation-based computer microtomography (SRCT), positron emission tomography (PET), PET-CT, magnetic resonance imaging (MRI), and ultrasound photoacoustic (USPA) can be used to assess Mg degradation and its effects in vitro/in vivo. However, these methods

Materials and Methods
In this pilot experiment, 15 12-week-old female Wistar rats were used. The animals were anesthetized with an intraperitoneal injection of 5 mg/kg Xylazine (Rompun Elanco, Italia, Florence, Italy) and 10 mg/kg Zoletil (Virbac, Opfikon, Gluttbrugg, Switzerland), while the depth of anesthesia was evaluated by the toe pinch response technique. Before surgery, the animal's legs were shaved using a depilatory cream (Veet, Reckitt Benckiser Healthcare (Italia), Milano, Italy) and carefully cleaned to avoid skin burns from contact with the cream. An incision was made laterally on the leg, and the muscles were carefully teased away to expose the diaphyseal region of the femur. A drill with a 1.55 mm diameter was used to create a transcortical hole in the femur. A low drilling rotational speed was Sensors 2023, 23, 2297 3 of 14 selected, and physiological saline (Fresenius Kabi, Verona, Italy) was dripped to minimize the frictional heat and thermal damage to the tissue. A pin implant with a length of 8 mm and a diameter of 1.6 mm made of either Mg-alloy (WE43) or Ti was implanted. The cylindrical implant was inserted by gentle tapping, resulting in a uniform press fit. After the pin placement, the wound site was cleaned with sterile cotton tips for the remaining bone debris, and the wound was closed with resorbable sutures (Johnson & Johnson Medical, Spa, Rome, Italy). The contralateral side was operated on similarly, using the same implant type. Figure 1 shows the implanted Mg pin in the CT image.
Healthcare (Italia), Milano, Italy) and carefully cleaned to avoid skin burns from conta the cream. An incision was made laterally on the leg, and the muscles were ca teased away to expose the diaphyseal region of the femur. A drill with a 1.55 mm d was used to create a transcortical hole in the femur. A low drilling rotational spe selected, and physiological saline (Fresenius Kabi,Verona, Italy) was dripped to m the frictional heat and thermal damage to the tissue. A pin implant with a length o and a diameter of 1.6 mm made of either Mg-alloy (WE43) or Ti was implanted. lindrical implant was inserted by gentle tapping, resulting in a uniform press fit. A pin placement, the wound site was cleaned with sterile cotton tips for the remainin debris, and the wound was closed with resorbable sutures (Johnson & Johnson M Spa, Rome, Italy). The contralateral side was operated on similarly, using the sa plant type. Figure 1 shows the implanted Mg pin in the CT image.

Experimental Workflow
Our study involved implanting pins into rat femurs. To determine the oxyge ration, we performed sequential NIRS and USPA acquisitions, followed by the app of MBLL on the NIRS data and of SPAX on the USPA data. We utilized PCA on th data to improve the presentation of the data for a short case study and a longi evaluation of the bone-healing process. Our approach combines NIRS and PCA a and USPA validation to provide a comprehensive evaluation of the spectral m ments. Additionally, a flowchart was created to illustrate the steps involved in our as shown in Figure 2. The flowchart provides a clear visualization of the processes out, starting from the implantation of pins and ending with the analysis of the s measurements. In this study, oxygen saturation was measured using both USPA an NIRS, resulting in the measurement of SO2 and StO2, respectively. The distinction b these two measurements arises from the differing principles and technologies util each method.

Experimental Workflow
Our study involved implanting pins into rat femurs. To determine the oxygen saturation, we performed sequential NIRS and USPA acquisitions, followed by the application of MBLL on the NIRS data and of SPAX on the USPA data. We utilized PCA on the NIRS data to improve the presentation of the data for a short case study and a longitudinal evaluation of the bone-healing process. Our approach combines NIRS and PCA analysis and USPA validation to provide a comprehensive evaluation of the spectral measurements. Additionally, a flowchart was created to illustrate the steps involved in our study, as shown in Figure 2. The flowchart provides a clear visualization of the processes carried out, starting from the implantation of pins and ending with the analysis of the spectral measurements. In this study, oxygen saturation was measured using both USPA and CW-NIRS, resulting in the measurement of SO 2 and StO 2 , respectively. The distinction between these two measurements arises from the differing principles and technologies utilized by each method.

NIRS Acquisition
NIRS acquisitions were made prior to surgery, immediately after surgery, and on days 3, 7, 14, and 45. The animals were anesthetized with isoflurane (2.5% in pure oxygen) and placed laterally on a stereo-foam platform to help prevent rapid heat loss. When necessary, the regrowth fur was removed using the depilatory cream (Veet) prior to the acquisition. In this case, the acquisition was made 2-3 min after shaving to account for possible changes in the skin microcirculation due to friction while shaving and cleaning. The acquisitions were always made in the same room, with an average temperature of 25 °C, and on reduced luminosity conditions to reduce background noise. Figure 3a illustrates the NIR probe placement, and Figure 3b shows the obtained raw spectra with multiple acquisitions. The NIRS optical probe used for this experiment, which was developed at our lab at Oslo Metropolitan University, Oslo, Norway, has a source-detector distance of 8 mm. This specific value was chosen for a 3-3.5 mm penetration depth at the implanttissue interface [29]. The optical light source of the probe operated in wavelengths between 650 and 1050 nm. To calculate the HbO2 and Hb, 740 nm and 840 nm wavelengths were chosen based on the prior differential path length factor (DPF) information from Geofrey D.V et al. [33]. The spectra data were collected from the Avantes Spectrometer (Avaspec-2048x14), which operates between 600 and 1100 nm.

NIRS Acquisition
NIRS acquisitions were made prior to surgery, immediately after surgery, and on days 3, 7, 14, and 45. The animals were anesthetized with isoflurane (2.5% in pure oxygen) and placed laterally on a stereo-foam platform to help prevent rapid heat loss. When necessary, the regrowth fur was removed using the depilatory cream (Veet) prior to the acquisition. In this case, the acquisition was made 2-3 min after shaving to account for possible changes in the skin microcirculation due to friction while shaving and cleaning. The acquisitions were always made in the same room, with an average temperature of 25 • C, and on reduced luminosity conditions to reduce background noise. Figure 3a illustrates the NIR probe placement, and Figure 3b shows the obtained raw spectra with multiple acquisitions. The NIRS optical probe used for this experiment, which was developed at our lab at Oslo Metropolitan University, Oslo, Norway, has a source-detector distance of 8 mm. This specific value was chosen for a 3-3.5 mm penetration depth at the implant-tissue interface [29]. The optical light source of the probe operated in wavelengths between 650 and 1050 nm. To calculate the HbO 2 and Hb, 740 nm and 840 nm wavelengths were chosen based on the prior differential path length factor (DPF) information from Geofrey D.V et al. [33]. The spectra data were collected from the Avantes Spectrometer (Avaspec-2048x14), which operates between 600 and 1100 nm.

NIRS Acquisition
NIRS acquisitions were made prior to surgery, immediately after surgery, and on days 3, 7, 14, and 45. The animals were anesthetized with isoflurane (2.5% in pure oxygen) and placed laterally on a stereo-foam platform to help prevent rapid heat loss. When necessary, the regrowth fur was removed using the depilatory cream (Veet) prior to the acquisition. In this case, the acquisition was made 2-3 min after shaving to account for possible changes in the skin microcirculation due to friction while shaving and cleaning. The acquisitions were always made in the same room, with an average temperature of 25 °C, and on reduced luminosity conditions to reduce background noise. Figure 3a illustrates the NIR probe placement, and Figure 3b shows the obtained raw spectra with multiple acquisitions. The NIRS optical probe used for this experiment, which was developed at our lab at Oslo Metropolitan University, Oslo, Norway, has a source-detector distance of 8 mm. This specific value was chosen for a 3-3.5 mm penetration depth at the implanttissue interface [29]. The optical light source of the probe operated in wavelengths between 650 and 1050 nm. To calculate the HbO2 and Hb, 740 nm and 840 nm wavelengths were chosen based on the prior differential path length factor (DPF) information from Geofrey D.V et al. [33]. The spectra data were collected from the Avantes Spectrometer (Avaspec-2048x14), which operates between 600 and 1100 nm.

Modified Beer-Lambert Law (MBLL)
The modified Beer-Lambert law (MBLL) is the foundation of CW NIRS [34]. MBLL can be used to model what is known as CW wavelength-dependent diffuse reflectance [35].
where I(λ) is the wavelength-dependent diffuse reflected light intensity, I 0 (λ) is the incident light, µ a (λ) is the absorbance of the tissue, d is the source-detector distance, the differential pathlength factor is DPF(λ), and the constant G is a medium-and geometrydependent constant. (1) can be written as: where OD(λ) stands for optical density. When more than one chromophore contributes to the total absorption µ a (λ), Equation (2) can be further rewritten as: where n is the number of chromophores, ε i (λ) is the extinction coefficient at the wavelength with the ith substance, and C i is the concentration of the given substance. Obtaining a total concentration estimate is impossible without knowledge of the geometry-dependent term. If the extinction coefficients ε i (λ) are known for individual wavelengths, and measurements are treated differentially in time, it will be possible to cancel out G because it is usually assumed to be constant. Changes in the concentration are of primary interest in NIRS and are independent of G, specifically in CW-NIRS, unlike in the frequency domain or the time domain NIRS [36]. It is hypothesized that, at times t1 and t2, the extinction coefficient ε i , DPF, D1, and G remain unchanged for measurements. The change in absorption is computed and removes factor G, resulting in a change in the concentration [36][37][38]. Equation (3) reduces to: where ∆ identifies the time-dependent changes. In order to approach the problem, at least two wavelengths are needed to calculate HbO 2 and Hb, which are, in principle, the only absorbing compounds that show a time-dependent modulation. By rewriting Equation (4) in matrix format, we will have: When measuring ∆OD from empirical measurements for the hemoglobin concentration, the above equation must be inverted. Please note that the a priori parameters of Equation (5) are the extinction coefficients of HbO 2 and Hb at the two wavelengths εi(λ) and the DPFs at the two wavelengths. The geometrical inter-optode distance d and the changes in optical densities ∆OD are measured empirically.
A measurement of the tissue perfusion StO 2 can be taken with NIRS by measuring changes in HbO 2 and Hb concentrations, using the following predictors of the Hb and HbO 2 relative concentrations: Due to the assumption that the tissue scattering and pathlength remain constant throughout the measurement period, CW-NIRS does not provide absolute oxygen saturation values. The modified Beer-Lambert law is used instead to provide a semiquantitative estimate.

Ultrasound and Photoacoustic Imaging
High-resolution Ultrasound (US) and Photoacoustic (PA) imaging (USPA) were acquired using the platform Vevo LAZR-X (FUJIFILM VisualSonics, Inc., Toronto, ON, Canada). The USPA imaging was performed sequentially after the NIRS measurement. This methodology was chosen to ensure that the results from the two techniques would be comparable and provide a comprehensive understanding of the samples. A linear US transducer array (MX 550) consisting of 256 elements at a nominal center frequency of 40 MHz and a bandwidth of 25-55 MHz is coupled with thin optical fibers and mounted on either side of the transducer. Homogenous light illumination is guaranteed by placing the sample to be imaged on the converging area of the two light beams. Spectral photoacoustic imaging (sPAI) was performed, within the wavelength range of 680-970 nm, with a 5 nm step. The imaging acquisition was made on days 3, 7, 28, and 45 after surgery. The rats were anesthetized with isoflurane (2-3% by volume with 0.8 L/min gas flow) and positioned in lateral recumbency, and the transducer was aligned perpendicularly to image the region of interest in the rats' hindlimbs.
The automated detection of the HbO 2 and Hb content was obtained from sPAI utilizing a newly developed superpixel data-driven unmixing (SPAX) framework, described in detail elsewhere [39]. The framework implements an SVD-based analysis to distinguish the relevant spectral information above the noise level automatically. SPAX is also extended to compensate for the spectral coloring artifact combining US image segmentation and spectral Monte Carlo (MC) light fluence simulations based on a predefined library of optical tissue properties. The advanced superpixel subsampling integrated within SPAX enables the detection of the least and most prominent components without a priori information.
Finally, the SO 2 has been calculated from the normalized unmixed maps of HbO 2 and Hb, obtained as the output of the SPAX analysis. Furthermore, the characteristic broad absorption spectrum of the metallic implant and its spatial distribution have also been obtained by the unsupervised SPAX approach.

Principal Component Analysis
Principal component analysis (PCA) was applied to NIRS data to extract practical information regarding the various factors affecting the Mg degradation. To perform exploratory analyses of NIRS data, PCA was applied on raw NIRS data. PCA is a mathematical procedure for resolving datasets into orthogonal components whose linear combinations approximate the original data by any desired degree of accuracy. The PCA method allows dominating patterns to be extracted from an NIRS data matrix. Two PCs were selected by examining the eigenvalues plot; outliers were detected and removed from the NIRS data after confirming their presence with spectral analysis. The dataset, including information about the implant types, rat group details, femur information (left and right), and timepoints (0, 3, 7, 14, and 45) was compiled. These data were preprocessed using normalization, one of the most commonly used preprocessing techniques. For subjects with damaged skin,

NIRS
StO 2 was measured on the implanted site pre-operatively (day 0) and 1, 3, 7, 14, and 45 days postoperatively. On day 0, two measurements were taken pre-operatively and post-operatively. For the simplicity of the visualization of the data, pre-surgery is chosen as day 0, and post-surgery is written as day 1. The StO 2 obtained from CW-NIRS for Mg-, Ti-, and sham-implanted rats is shown in Figure 4. Despite the reduced number of animals used for Ti-implanted and sham animals, it seems that Mg-implanted animals present a higher variability at the initial timepoints. The proposed study compared the spectroscopic characteristics of different implanted rats to assess StO 2 .
information about the implant types, rat group details, femur information (left and right), and timepoints (0, 3, 7, 14, and 45) was compiled. These data were preprocessed using normalization, one of the most commonly used preprocessing techniques. For subjects with damaged skin, a separate PCA was performed. In our study, PCA was performed using the open-source software R, in Rstudio.

NIRS
StO2 was measured on the implanted site pre-operatively (day 0) and 1, 3, 7, 14, and 45 days postoperatively. On day 0, two measurements were taken pre-operatively and post-operatively. For the simplicity of the visualization of the data, pre-surgery is chosen as day 0, and post-surgery is written as day 1. The StO2 obtained from CW-NIRS for Mg-, Ti-, and sham-implanted rats is shown in Figure 4. Despite the reduced number of animals used for Ti-implanted and sham animals, it seems that Mg-implanted animals present a higher variability at the initial timepoints. The proposed study compared the spectroscopic characteristics of different implanted rats to assess StO2.

NIRS and USPA-Spectral Analysis
The NIRS spectral region exhibited typical differences in the spectra of Hb and HbO2. Figure 4 shows how Hb and HbO2 have different wavelength dependences regarding extinction coefficients. The DPF values for the wavelength at 740 nm and 840 nm are 3.50 and 3.01, respectively, which are used to obtain the relative information about Hb and HbO2 based on the literature [33]. The wavelength dependency of blood absorption can be used to determine the blood StO2 level. The blue curve in Figure 5a represents the extinction coefficient of Hb, and the red and green curves represent the extinction coefficient of HbO2 and THb, respectively. Figure 5b shows the unmixing of the Hb, HbO2, and Mg pin from PAI. Figure 5c,d show a semi-quantitative analysis of the oxygen saturation calculated from spectral photoacoustic unmixing and NIRS. Here, we focused on NIRS evaluations, and USPA has been used to identify the anatomical structures and validate the molecular evaluations extracted from the entire region of interest. The graphs show a typical pattern of longitudinal variation in StO2 in the soft tissue around Mg and Ti implants. Similar trends have been retrieved from NIRS and USPA.

NIRS and USPA-Spectral Analysis
The NIRS spectral region exhibited typical differences in the spectra of Hb and HbO 2 . Figure 4 shows how Hb and HbO 2 have different wavelength dependences regarding extinction coefficients. The DPF values for the wavelength at 740 nm and 840 nm are 3.50 and 3.01, respectively, which are used to obtain the relative information about Hb and HbO 2 based on the literature [33]. The wavelength dependency of blood absorption can be used to determine the blood StO 2 level. The blue curve in Figure 5a represents the extinction coefficient of Hb, and the red and green curves represent the extinction coefficient of HbO 2 and THb, respectively. Figure 5b shows the unmixing of the Hb, HbO 2 , and Mg pin from PAI. Figure 5c,d show a semi-quantitative analysis of the oxygen saturation calculated from spectral photoacoustic unmixing and NIRS. Here, we focused on NIRS evaluations, and USPA has been used to identify the anatomical structures and validate the molecular evaluations extracted from the entire region of interest. The graphs show a typical pattern of longitudinal variation in StO 2 in the soft tissue around Mg and Ti implants. Similar trends have been retrieved from NIRS and USPA.
We used USPA imaging to study the possible presence of bubbles at the implant-tissue interface as a factor contributing to the higher variation in SO 2 in the surrounding soft tissue of the Mg implant on day 3. Figure 6a,b show the ultrasound and photoacoustic images of the implanted rat femur at day 3, where the tip of the Mg pin is depicted in the short axes view. Figure 6c shows the spatial distribution of the unmixed components such as the HbO 2 , Hb, and Mg pin. We used USPA imaging to study the possible presence of bubbles at the implanttissue interface as a factor contributing to the higher variation in SO2 in the surrounding soft tissue of the Mg implant on day 3. Figure 6a,b show the ultrasound and photoacoustic images of the implanted rat femur at day 3, where the tip of the Mg pin is depicted in the short axes view. Figure 6c shows the spatial distribution of the unmixed components such as the HbO2, Hb, and Mg pin.   We used USPA imaging to study the possible presence of bubbles at the implanttissue interface as a factor contributing to the higher variation in SO2 in the surrounding soft tissue of the Mg implant on day 3. Figure 6a,b show the ultrasound and photoacoustic images of the implanted rat femur at day 3, where the tip of the Mg pin is depicted in the short axes view. Figure 6c shows the spatial distribution of the unmixed components such as the HbO2, Hb, and Mg pin. Figure 6. (a,b) The Ultrasound and Photoacoustic images of the Mg-implanted rat's femur on day 3 after surgery in grey and red scales, respectively; (c) Overlapped unmixed distribution maps of the Oxy-, Deoxy-hemoglobin, and Mg pin in red, green, and blue scales, respectively, automatically obtained from sPAI. The scale bar size is 2 mm. Figure 6. (a,b) The Ultrasound and Photoacoustic images of the Mg-implanted rat's femur on day 3 after surgery in grey and red scales, respectively; (c) Overlapped unmixed distribution maps of the Oxy-, Deoxy-hemoglobin, and Mg pin in red, green, and blue scales, respectively, automatically obtained from sPAI. The scale bar size is 2 mm.

Case Study
On day 3, one of the Ti-implanted rats developed a skin rash as an allergic reaction to the shaving cream that persisted until the end of the study. We found a measurable difference by analyzing the StO 2 values and comparing a Ti-implanted animal with normal skin to a rat with skin rash. The data obtained at different timepoints were also visualized Sensors 2023, 23, 2297 9 of 14 using PCA. In Figure 7, the PCA score plot shows the effect of damaged skin in terms of correlation at Timepoints 3, 7, and 14.

Case Study
On day 3, one of the Ti-implanted rats developed a skin rash as an allergic reaction to the shaving cream that persisted until the end of the study. We found a measurable difference by analyzing the StO2 values and comparing a Ti-implanted animal with normal skin to a rat with skin rash. The data obtained at different timepoints were also visualized using PCA. In Figure 7, the PCA score plot shows the effect of damaged skin in terms of correlation at Timepoints 3, 7, and 14.

Longitudinal Evaluation of Healing
Furthermore, to assess the evolution of healing, we compared the measurements of the last timepoint, day 45, with the measurements performed before the surgery, day 0. The PCA score plot, represented in Figure 8, shows a significant spectral correlation at day 45 with day 0 on the Mg-implanted rats. Improbably, the Ti and Sham animals present a less significant correlation between the same timepoints. The same trend was observed in terms of the StO2 values of Mg-implanted rats; day 45 presented StO2 values similar to those of day 0. Although preliminary, these results suggest that there is a difference between Mg-implanted animals and Ti-implanted or sham animals.

Longitudinal Evaluation of Healing
Furthermore, to assess the evolution of healing, we compared the measurements of the last timepoint, day 45, with the measurements performed before the surgery, day 0. The PCA score plot, represented in Figure 8, shows a significant spectral correlation at day 45 with day 0 on the Mg-implanted rats. Improbably, the Ti and Sham animals present a less significant correlation between the same timepoints. The same trend was observed in terms of the StO 2 values of Mg-implanted rats; day 45 presented StO 2 values similar to those of day 0. Although preliminary, these results suggest that there is a difference between Mg-implanted animals and Ti-implanted or sham animals.

Case Study
On day 3, one of the Ti-implanted rats developed a skin rash as an allergic reaction to the shaving cream that persisted until the end of the study. We found a measurable difference by analyzing the StO2 values and comparing a Ti-implanted animal with normal skin to a rat with skin rash. The data obtained at different timepoints were also visualized using PCA. In Figure 7, the PCA score plot shows the effect of damaged skin in terms of correlation at Timepoints 3, 7, and 14.

Longitudinal Evaluation of Healing
Furthermore, to assess the evolution of healing, we compared the measurements of the last timepoint, day 45, with the measurements performed before the surgery, day 0. The PCA score plot, represented in Figure 8, shows a significant spectral correlation at day 45 with day 0 on the Mg-implanted rats. Improbably, the Ti and Sham animals present a less significant correlation between the same timepoints. The same trend was observed in terms of the StO2 values of Mg-implanted rats; day 45 presented StO2 values similar to those of day 0. Although preliminary, these results suggest that there is a difference between Mg-implanted animals and Ti-implanted or sham animals.

Discussion
The modified Beer-Lambert approach is extensively used in the biomedical optics community due to its simplicity [35]. Researchers have used CW light to measure blood oxygenation and blood volume changes over time [24,37]. The present paper extends the modified Beer-Lambert approach to calculate the oxygen saturation of the tissues surrounding an implant. The NIR spectrometer Avaspec (Avantes, BV) can be used to measure the StO 2 levels in the soft tissue located under a sensor probe to measure the oxygen content of the hemoglobin in the soft tissue. The spectra are captured in real time by radiating broadband NIR light, and only two selective wavelengths (740 nm and 850 nm) were used in MBLL to measure changes in HbO 2 and Hb. Based on diffusion theory, it is possible to calculate the depth to which diffuse light will penetrate tissue as a function of the source-detector separation (d). Using a simple dependence, Weiss found that the photon depth before being detected is proportional to the square root of the source-detector separation (d) [40]. On average, the penetration depth of photons in the tissue is around 1/2 to 1/3 of the source-detector distance [41]. NIR light is estimated to reach a 3-3.5 mm depth, and the diffuse light is detected by the optical fiber inside the probe [29,42]. The same optical probe was recently used to validate the spectral absorption curves obtained from USPA [43]. As shown in Figure 5, we have used the molar extinction coefficient values to estimate the change in Hb and HbO 2 using an optical probe developed at Oslo Metropolitan University, Oslo, Norway [29]. In order to investigate different wavelengths, we must have DPF values for each wavelength. Minor changes in DPF values could result in incorrect results [44]. It is assumed that these changes are minor, and, thus, a DPF value was chosen based on the literature that uses a DPF value based on the source-detector distance we selected.
NIRS studies have shown that oxygenation changes in the expected direction; however, absolute values can vary among studies and devices [45,46]. While CW-NIRS, such as the one used in this study, cannot estimate absolute concentrations, they are able to provide relative changes compared to a baseline, unlike FD-NIRS and TD-NIRS. The StO 2 differences between some of the most commonly used commercial NIRS devices typically range from 10 to 15%, but they can be as high as 20% at low StO 2 levels [46]. As a result of this variability across devices, it is challenging to establish thresholds for StO 2 that can guide clinical management. Several equations were recently derived from converting values from one device to another to standardize oxygenation measurements across devices [45]. However, the StO 2 values obtained through the NIRS probe, as reported in the proposed paper, are in line with the measurements obtained from USPA. One phenomenon associated with Mg implants degradation is the formation of gas bubbles around the implantation site, particularly at early timepoints after implantation, such as day 1 and day 3. This is challenging to measure with USPA, but NIRS presents a significant advantage in this sense. Therefore, NIRS can be used to investigate the bubble formation behavior of StO 2, particularly in the case of Mg alloy implantation. Upon implantation, magnesium and its alloys degrade in the body, releasing corrosion products such as H 2 in the local environment [47]. For the in vivo study, maximum gas volumes were formed from earlier days until day 5 [48]. Rats implanted with Mg had the highest StO 2 variation on days 1 and 3 relative to their baseline values on day 0 compared to rats implanted with Ti or sham implants. Ultrasound (US) and photoacoustic (PA) imaging technology has been used to assess the SO 2 changes in the vicinity of the implant. The combination of USPA with a recently developed unsupervised unmixing framework named superpixel photoacoustic unmixing (SPAX) has enabled the automated detection of the Mg-based implant, HbO 2 , and Hb as a prominent absorber [39]. Thus, this methodology was used as a comparison to benchmark the NIRS assessments in vivo. Although the sPAI unmixing provides results about the molecular tissue components' spectra and their distribution maps, the SO 2 evaluation is not an absolute measure. Thus, to obtain the absolute quantification in PA imaging, an improved measurement of the system response, optical tissue properties, and Grüneisen parameters are required. In the future, we aim to address the absolute quantification by implementing deep learning approaches based on non-explicit light fluence estimation, leading to high-fidelity SO 2 estimations.
There have been a few studies that suggest that StO 2 levels are significantly affected by the skin blood flow. NIRS measurements were shown to be affected by the skin blood flow by Buono et al. [49]. Our case study results showed that the animal with the skin rash presented a higher StO 2 level associated with the abnormally high blood flow to the injured area. Furthermore, PCA was used in our study to demonstrate the potential for effectively differentiating between the spectral signatures collected from healthy and abnormal skin conditions. The results, although limited to one case, suggest the potential for PCA to be used in future studies to differentiate between healthy and diseased tissue. On a last note, our study uses albino rats, and the skin rash is easily detectable by visual observation; yet, NIRS could have more meaningful use in cases where skin pigmentation is higher and, thus, it is more difficult to detect changes visually.
In this study, we used PCA to detect differences between the timepoints (0, 1, 3, 7, 14, and 45). The PCA score plot for days 0 and 45 for all rats can be seen in Figure 7. Interestingly, on day 45, the rats implanted with Mg seemed closer to their pre-implanted state, day 0, when compared to the rats of the other groups. Moreover, the StO 2 values of days 0 and 45 for the Mg-implanted animals were similar. This result seems to be in accordance with recent studies showing that Mg implants' degradation promotes tissue regeneration and leads to a faster soft tissue homogeneity [47,50]. Although preliminary, our study shows that NIRS and PCA can detect these changes and are suitable tools for monitoring Mg implants degradation, particularly in an initial stage of soft tissue regeneration.
Our study presents a purely descriptive pilot study. However, to our knowledge, this study is the first longitudinal study using NIRS and PCA to assess, in vivo, the implant soft tissue-interface. With our NIR optical probe, we demonstrated that StO 2 mainly changed postoperatively from day 0 to day 3, possibly due to bubble gas formation, a wellknown side effect associated with the initial fast degradation of Mg implants. By using our approach, it is demonstrated that StO 2 changes over time after implantation and that PCA can detect meaningful correlations with physiological reasoning. Further experiments with a larger group of animals should be conducted in order to significantly validate our findings. Furthermore, NIRS combined with multivariate techniques such as PLS and PCA and complemented with morphological information from USPA can provide a quick, objective, and reliable measure of the implant-tissue interface.

Conclusions
Applying the modified Beer-Lambert law (MBLL) to particular measurement conditions related to the effect of Mg degradation within tissues can enhance the reliability of data on the target tissue's physiological state and biochemical content. NIRS is a nondestructive, non-invasive technique used to monitor tissue oxygenation in various clinical settings. This study shows that it may be a valuable method for measuring tissue oxygen levels and monitoring the tissue healing associated with Mg implant degradation. We use NIR spectroscopy techniques along with PCA analysis to assess the tissues surrounding the implant-tissue interface over time and detect significant changes. By combining NIRS and USPA, many other tissue parameters can be measured non-destructively and noninvasively. Furthermore, NIRS combined with multivariate techniques such as PLS and PCA and complemented with morphological information from USPA can provide a quick, objective, and reliable measure of the implant-tissue interface.